Verified answer

1.

a) (y+1)/y

[tex] \frac{ {y}^{2} + y }{ {y}^{2} } = \frac{y(y + 1)}{ {y}^{2} } = \frac{y + 1}{y} [/tex]

b) a/a+2

[tex] \frac{ {a}^{2} - 2a }{ {a}^{2} - 4 } = \frac{a(a - 2)}{(a - 2)(a + 2)} = \frac{a}{a + 2} [/tex]

2.

a) (a²+15)/(a²+5a)

[tex] \frac{3}{a} + \frac{a - 3}{a + 5} = \frac{3a + 15 + {a}^{2} - 3a }{a(a + 5)} = \frac{ {a}^{2} + 15 }{ {a}^{2} + 5a } [/tex]

b) 4x/x²-4

[tex] \frac{ {2x}^{2} }{ {x }^{2} - 4 } - \frac{2x}{x + 2} = \frac{ {2x}^{2} - {2x}^{2} + 4x }{(x - 2)(x + 2)} = \frac{4x}{ {x}^{2} - 4 } [/tex]

3. 7

[tex] \frac{ {y}^{2} - 6y + 9 }{ {y}^{2} - 9 } \div \frac{10y - 30}{ {y}^{2} + 3y } = \frac{ {(y - 3)}^{2} }{(y - 3)(y + 3)} \times \frac{y(y + 3)}{10(y - 3)} = \frac{y}{10} [/tex]

При у равно 70

[tex] \frac{y}{10} = \frac{70}{10} = 7[/tex]